Oscillatory behavior in linear difference equations under unmodeled dynamics and parametrical errors

Abstract

This paper investigates the presence of oscillating solutions in time-varying difference equations even in the case when there exist parametrical errors (i.e., errors in the sequences defining their coefficients) and/or unmodeled dynamics, namely, the current order is unknown and greater than the nominal known order. The formulation is related to the concepts of conjugacy, disconjugacy, positivity, and generalized zeros and general conditions of oscillation are obtained both over particular intervals and for the whole solution. Some results concerned with the presence of stable oscillations are also presented.